संख्या रेखा पर \(\sqrt{37}-6\) किस दो पूर्णांकों के बीच होगा?
Between which two integers will \(\sqrt{37}-6\) lie on the number line?
#number-line
#square-root
#interval
#reasoning
A (0) और (1) / (0) and (1)
B (1) और (2) / (1) and (2)
C (-1) और (0) / (-1) and (0)
D (-2) और (-1) / (-2) and (-1)
Explanation opens after your attempt
Correct Answer
A. (0) और (1) / (0) and (1)
Step 1
Concept
Since \(6^2<37<7^2\), \(6<\sqrt{37}<7\) and \(0<\sqrt{37}-6<1\). Subtract the same number from a root interval to locate the value.
Step 2
Why this answer is correct
The correct answer is A. (0) और (1) / (0) and (1). Since \(6^2<37<7^2\), \(6<\sqrt{37}<7\) and \(0<\sqrt{37}-6<1\). Subtract the same number from a root interval to locate the value.
Step 3
Exam Tip
क्योंकि \(6^2<37<7^2\), इसलिए \(6<\sqrt{37}<7\) और \(0<\sqrt{37}-6<1\) है। वर्गमूल वाले अंतराल में समान संख्या घटाकर स्थिति पाएं।
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संख्या रेखा पर (3) के सापेक्ष (4.6) का सममित बिंदु कौन सा होगा?
What will be the point symmetric to (4.6) with respect to (3) on the number line?
#number-line
#symmetry
#midpoint
#decimals
A (1.4)
B (2.4)
C (3.4)
D (5.6)
Explanation opens after your attempt
Step 1
Concept
For the symmetric point (3) is the midpoint so the other point is \(2\times3-4.6=1.4\). In symmetry the midpoint is equally distant from both endpoints.
Step 2
Why this answer is correct
The correct answer is A. (1.4). For the symmetric point (3) is the midpoint so the other point is \(2\times3-4.6=1.4\). In symmetry the midpoint is equally distant from both endpoints.
Step 3
Exam Tip
सममित बिंदु के लिए (3) मध्य बिंदु होगा इसलिए दूसरा बिंदु \(2\times3-4.6=1.4\) है। सममिति में मध्य बिंदु दोनों सिरों से बराबर दूरी पर होता है।
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संख्या रेखा पर \(\sqrt{24}\) के बारे में कौन सा कथन गलत है?
Which statement about \(\sqrt{24}\) on the number line is false?
#number-line
#common-mistake
#square-root
#false-statement
A \(\sqrt{24}\) (4) और (5) के बीच है / \(\sqrt{24}\) is between (4) and (5)
B \(\sqrt{24}<5\)
C \(\sqrt{24}>4\)
D \(\sqrt{24}=24\)
Explanation opens after your attempt
Correct Answer
D. \(\sqrt{24}=24\)
Step 1
Concept
Since \(4^2<24<5^2\), \(\sqrt{24}\) is between (4) and (5) and is not equal to (24). Do not treat a square root as the original number.
Step 2
Why this answer is correct
The correct answer is D. \(\sqrt{24}=24\). Since \(4^2<24<5^2\), \(\sqrt{24}\) is between (4) and (5) and is not equal to (24). Do not treat a square root as the original number.
Step 3
Exam Tip
क्योंकि \(4^2<24<5^2\), इसलिए \(\sqrt{24}\) (4) और (5) के बीच है और (24) के बराबर नहीं है। वर्गमूल को मूल संख्या न मानें।
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संख्या रेखा पर \(-\sqrt{0.81}\) की (0) से दूरी कितनी है?
What is the distance of \(-\sqrt{0.81}\) from (0) on the number line?
#number-line
#distance
#decimal-root
#absolute-value
A (0.09)
B (0.9)
C (1.8)
D (9)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{0.81}=0.9\), so the distance of \(-\sqrt{0.81}\) from (0) is (0.9). Distance equals magnitude.
Step 2
Why this answer is correct
The correct answer is B. (0.9). \(\sqrt{0.81}=0.9\), so the distance of \(-\sqrt{0.81}\) from (0) is (0.9). Distance equals magnitude.
Step 3
Exam Tip
\(\sqrt{0.81}=0.9\), इसलिए \(-\sqrt{0.81}\) की (0) से दूरी (0.9) है। दूरी परिमाण के बराबर होती है।
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संख्या रेखा पर \(-\sqrt{25}\) और \(-\sqrt{36}\) में कौन सा बिंदु दाईं ओर होगा?
On the number line, which point will be to the right, \(-\sqrt{25}\) or \(-\sqrt{36}\)?
#number-line
#negative-roots
#comparison
#order
A \(-\sqrt{25}\)
B \(-\sqrt{36}\)
C दोनों समान हैं / Both are equal
D दोनों धनात्मक हैं / Both are positive
Explanation opens after your attempt
Correct Answer
A. \(-\sqrt{25}\)
Step 1
Concept
\(-\sqrt{25}=-5\) and \(-\sqrt{36}=-6\), so (-5) is to the right. Among negatives, the one with smaller magnitude is greater.
Step 2
Why this answer is correct
The correct answer is A. \(-\sqrt{25}\). \(-\sqrt{25}=-5\) and \(-\sqrt{36}=-6\), so (-5) is to the right. Among negatives, the one with smaller magnitude is greater.
Step 3
Exam Tip
\(-\sqrt{25}=-5\) और \(-\sqrt{36}=-6\), इसलिए (-5) दाईं ओर है। ऋणात्मक संख्याओं में कम परिमाण वाली संख्या बड़ी होती है।
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इनमें से कौन सा मान संख्या रेखा पर (2) के सबसे निकट है?
Which of these values is closest to (2) on the number line?
#number-line
#closeness
#square-root
#estimation
A \(\sqrt{3}\)
B \(\sqrt{5}\)
C \(\sqrt{6}\)
D (1.2)
Explanation opens after your attempt
Correct Answer
B. \(\sqrt{5}\)
Step 1
Concept
\(\sqrt{5}\approx2.24\), which is closest to (2) among the options. Compare each distance for closeness.
Step 2
Why this answer is correct
The correct answer is B. \(\sqrt{5}\). \(\sqrt{5}\approx2.24\), which is closest to (2) among the options. Compare each distance for closeness.
Step 3
Exam Tip
\(\sqrt{5}\approx2.24\), जो दिए गए विकल्पों में (2) के सबसे पास है। निकटता के लिए प्रत्येक दूरी की तुलना करें।
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संख्या रेखा पर \(\frac{13}{4}\) को (3) और (4) के बीच कहां रखा जाएगा?
Where will \(\frac{13}{4}\) be placed between (3) and (4) on the number line?
#number-line
#improper-fraction
#equal-parts
#position
A (3) के बाद पहला चौथाई बिंदु / First quarter point after (3)
B (3) के बाद दूसरा चौथाई बिंदु / Second quarter point after (3)
C (3) के बाद तीसरा चौथाई बिंदु / Third quarter point after (3)
D ठीक (4) पर / Exactly at (4)
Explanation opens after your attempt
Correct Answer
A. (3) के बाद पहला चौथाई बिंदु / First quarter point after (3)
Step 1
Concept
\(\frac{13}{4}=3+\frac{1}{4}\), so it is the first quarter point after (3). Think of improper fractions as mixed numbers.
Step 2
Why this answer is correct
The correct answer is A. (3) के बाद पहला चौथाई बिंदु / First quarter point after (3). \(\frac{13}{4}=3+\frac{1}{4}\), so it is the first quarter point after (3). Think of improper fractions as mixed numbers.
Step 3
Exam Tip
\(\frac{13}{4}=3+\frac{1}{4}\), इसलिए यह (3) के बाद पहले चौथाई बिंदु पर होगा। अशुद्ध भिन्न को मिश्रित रूप में सोचें।
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संख्या रेखा पर \(-\sqrt{4}\) और \(\sqrt{16}\) के मध्य बिंदु का मान क्या है?
What is the midpoint of \(-\sqrt{4}\) and \(\sqrt{16}\) on the number line?
#number-line
#midpoint
#roots
#average
A (0)
B (1)
C (2)
D (3)
Explanation opens after your attempt
Step 1
Concept
\(-\sqrt{4}=-2\) and \(\sqrt{16}=4\), so the midpoint is \(\frac{-2+4}{2}=1\). Simplify roots first.
Step 2
Why this answer is correct
The correct answer is B. (1). \(-\sqrt{4}=-2\) and \(\sqrt{16}=4\), so the midpoint is \(\frac{-2+4}{2}=1\). Simplify roots first.
Step 3
Exam Tip
\(-\sqrt{4}=-2\) और \(\sqrt{16}=4\), इसलिए मध्य बिंदु \(\frac{-2+4}{2}=1\) है। पहले वर्गमूल सरल करें।
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संख्या रेखा पर \(\sqrt{1}\), \(\sqrt{2}\), और \(\sqrt{3}\) का बढ़ता क्रम क्या है?
What is the increasing order of \(\sqrt{1}\), \(\sqrt{2}\), and \(\sqrt{3}\) on the number line?
#number-line
#square-root
#increasing-order
#comparison
A \(\sqrt{3},\sqrt{2},\sqrt{1}\)
B \(\sqrt{1},\sqrt{2},\sqrt{3}\)
C \(\sqrt{2},\sqrt{1},\sqrt{3}\)
D \(\sqrt{1},\sqrt{3},\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
B. \(\sqrt{1},\sqrt{2},\sqrt{3}\)
Step 1
Concept
For positive numbers, (1<2<3) gives \(\sqrt{1}<\sqrt{2}<\sqrt{3}\). Square root preserves order.
Step 2
Why this answer is correct
The correct answer is B. \(\sqrt{1},\sqrt{2},\sqrt{3}\). For positive numbers, (1<2<3) gives \(\sqrt{1}<\sqrt{2}<\sqrt{3}\). Square root preserves order.
Step 3
Exam Tip
धनात्मक संख्याओं के लिए (1<2<3) होने पर \(\sqrt{1}<\sqrt{2}<\sqrt{3}\) है। वर्गमूल क्रम को बनाए रखता है।
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इनमें से कौन सा बिंदु संख्या रेखा पर (-2) से बाईं ओर होगा?
Which of these points will lie to the left of (-2) on the number line?
#number-line
#left-right
#negative-irrational
#comparison
A \(-\sqrt{6}\)
B \(-\sqrt{3}\)
C (-1.9)
D \(-\frac{3}{2}\)
Explanation opens after your attempt
Correct Answer
A. \(-\sqrt{6}\)
Step 1
Concept
\(\sqrt{6}\approx2.45\), so \(-\sqrt{6}\approx-2.45\), which is left of (-2). The smaller number lies to the left.
Step 2
Why this answer is correct
The correct answer is A. \(-\sqrt{6}\). \(\sqrt{6}\approx2.45\), so \(-\sqrt{6}\approx-2.45\), which is left of (-2). The smaller number lies to the left.
Step 3
Exam Tip
\(\sqrt{6}\approx2.45\), इसलिए \(-\sqrt{6}\approx-2.45\) है जो (-2) से बाईं ओर है। छोटी संख्या बाईं ओर होती है।
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यदि बिंदु (P), (-0.4) से \(\sqrt{0.04}\) इकाई दाईं ओर है तो (P) का मान क्या होगा?
If point (P) is \(\sqrt{0.04}\) unit to the right of (-0.4), what will be the value of (P)?
#number-line
#movement
#decimal-root
#negative-numbers
A (-0.6)
B (-0.2)
C (0.2)
D (0.6)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{0.04}=0.2\), so (P=-0.4+0.2=-0.2). Moving right means addition.
Step 2
Why this answer is correct
The correct answer is B. (-0.2). \(\sqrt{0.04}=0.2\), so (P=-0.4+0.2=-0.2). Moving right means addition.
Step 3
Exam Tip
\(\sqrt{0.04}=0.2\), इसलिए (P=-0.4+0.2=-0.2) है। दाईं ओर जाने पर जोड़ते हैं।
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यदि \(\sqrt{a}\) संख्या रेखा पर ठीक (4.5) पर है तो (a) का मान क्या होगा?
If \(\sqrt{a}\) is exactly at (4.5) on the number line, what will be the value of (a)?
#number-line
#square-root
#equation
#decimals
A (9)
B (18)
C (20.25)
D (22.5)
Explanation opens after your attempt
Correct Answer
C. (20.25)
Step 1
Concept
If \(\sqrt{a}=4.5\), then (a=(4.5)2 =20.25). Square both sides to remove the square root.
Step 2
Why this answer is correct
The correct answer is C. (20.25). If \(\sqrt{a}=4.5\), then (a=(4.5)2 =20.25). Square both sides to remove the square root.
Step 3
Exam Tip
\(\sqrt{a}=4.5\) होने पर (a=(4.5)2 =20.25) है। वर्गमूल हटाने के लिए वर्ग करें।
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संख्या रेखा पर \(\frac{2}{5}\) और \(\frac{7}{10}\) के बीच की दूरी कितनी है?
What is the distance between \(\frac{2}{5}\) and \(\frac{7}{10}\) on the number line?
#number-line
#distance
#fractions
#rational-numbers
A \(\frac{1}{10}\)
B \(\frac{2}{10}\)
C \(\frac{3}{10}\)
D \(\frac{9}{10}\)
Explanation opens after your attempt
Correct Answer
C. \(\frac{3}{10}\)
Step 1
Concept
\(\frac{2}{5}=\frac{4}{10}\), so the distance is \(\frac{7}{10}-\frac{4}{10}=\frac{3}{10}\). Use a common denominator before subtracting.
Step 2
Why this answer is correct
The correct answer is C. \(\frac{3}{10}\). \(\frac{2}{5}=\frac{4}{10}\), so the distance is \(\frac{7}{10}-\frac{4}{10}=\frac{3}{10}\). Use a common denominator before subtracting.
Step 3
Exam Tip
\(\frac{2}{5}=\frac{4}{10}\), इसलिए दूरी \(\frac{7}{10}-\frac{4}{10}=\frac{3}{10}\) है। समान हर बनाकर घटाएं।
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इनमें से कौन सा मान संख्या रेखा पर (0) और (1) के बीच नहीं होगा?
Which of these values will not lie between (0) and (1) on the number line?
#number-line
#between
#real-numbers
#comparison
A \(\frac{\sqrt{2}}{2}\)
B \(\frac{5}{6}\)
C (-0.1)
D \(\sqrt{0.25}\)
Explanation opens after your attempt
Step 1
Concept
(-0.1) is less than zero, so it is not between (0) and (1). Compare with both bounds when checking between values.
Step 2
Why this answer is correct
The correct answer is C. (-0.1). (-0.1) is less than zero, so it is not between (0) and (1). Compare with both bounds when checking between values.
Step 3
Exam Tip
(-0.1) शून्य से छोटा है इसलिए (0) और (1) के बीच नहीं है। बीच की जांच में दोनों सीमाओं से तुलना करें।
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संख्या रेखा पर \(\sqrt{\frac{1}{2}}\) का सबसे अच्छा दशमलव अनुमान कौन सा है?
What is the best decimal estimate of \(\sqrt{\frac{1}{2}}\) on the number line?
#number-line
#square-root
#fraction
#estimation
A (0.5)
B (0.707)
C (1.2)
D (2)
Explanation opens after your attempt
Correct Answer
B. (0.707)
Step 1
Concept
\(\sqrt{\frac{1}{2}}\approx0.707\). In estimation, you can square the options to check.
Step 2
Why this answer is correct
The correct answer is B. (0.707). \(\sqrt{\frac{1}{2}}\approx0.707\). In estimation, you can square the options to check.
Step 3
Exam Tip
\(\sqrt{\frac{1}{2}}\approx0.707\) होता है। अनुमान में वर्ग करके विकल्प जांच सकते हैं।
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पिछले प्रश्न जैसी रेखा में (2) से चौथा बराबर बिंदु कौन सा होगा जब प्रत्येक भाग \(\frac{1}{2}\) हो?
In a similar segment, what is the fourth equal point from (2) when each part is \(\frac{1}{2}\)?
#number-line
#equal-steps
#fractions
#position
A (3)
B (3.5)
C (4)
D (4.5)
Explanation opens after your attempt
Step 1
Concept
The fourth point is \(2+4\times\frac{1}{2}=4\). Add the total step length to the starting point.
Step 2
Why this answer is correct
The correct answer is C. (4). The fourth point is \(2+4\times\frac{1}{2}=4\). Add the total step length to the starting point.
Step 3
Exam Tip
चौथा बिंदु \(2+4\times\frac{1}{2}=4\) है। बराबर भागों में आरंभिक बिंदु में कुल कदम जोड़ें।
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यदि (2) से (5) तक की दूरी को (6) बराबर भागों में बांटा जाए तो प्रत्येक भाग की लंबाई क्या होगी?
If the distance from (2) to (5) is divided into (6) equal parts, what is the length of each part?
#number-line
#equal-parts
#distance
#fractions
A \(\frac{1}{3}\)
B \(\frac{1}{2}\)
C (1)
D (3)
Explanation opens after your attempt
Correct Answer
B. \(\frac{1}{2}\)
Step 1
Concept
The total distance is (5-2=3), and each part is \(\frac{3}{6}=\frac{1}{2}\). Find the total distance first.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{1}{2}\). The total distance is (5-2=3), and each part is \(\frac{3}{6}=\frac{1}{2}\). Find the total distance first.
Step 3
Exam Tip
कुल दूरी (5-2=3) है और प्रत्येक भाग \(\frac{3}{6}=\frac{1}{2}\) होगा। पहले कुल दूरी निकालें।
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संख्या रेखा पर \(\sqrt{15}\) और (4) के बीच कौन सा संबंध सही है?
Which relation between \(\sqrt{15}\) and (4) is correct on the number line?
#number-line
#square-root
#comparison
#inequality
A \(\sqrt{15}<4\)
B \(\sqrt{15}=4\)
C \(\sqrt{15}>4\)
D \(\sqrt{15}=15\)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{15}<4\)
Step 1
Concept
Since (15<16), \(\sqrt{15}<4\). Compare using the nearby perfect square.
Step 2
Why this answer is correct
The correct answer is A. \(\sqrt{15}<4\). Since (15<16), \(\sqrt{15}<4\). Compare using the nearby perfect square.
Step 3
Exam Tip
क्योंकि (15<16), इसलिए \(\sqrt{15}<4\) है। तुलना के लिए पूर्ण वर्ग से मिलाएं।
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संख्या रेखा पर \(1-\sqrt{3}\) किस दो पूर्णांकों के बीच होगा?
Between which two integers will \(1-\sqrt{3}\) lie on the number line?
#number-line
#irrational-numbers
#subtraction
#estimation
A (-2) और (-1) / (-2) and (-1)
B (-1) और (0) / (-1) and (0)
C (0) और (1) / (0) and (1)
D (1) और (2) / (1) and (2)
Explanation opens after your attempt
Correct Answer
B. (-1) और (0) / (-1) and (0)
Step 1
Concept
\(\sqrt{3}\approx1.73\), so \(1-\sqrt{3}\approx-0.73\). It lies between (-1) and (0).
Step 2
Why this answer is correct
The correct answer is B. (-1) और (0) / (-1) and (0). \(\sqrt{3}\approx1.73\), so \(1-\sqrt{3}\approx-0.73\). It lies between (-1) and (0).
Step 3
Exam Tip
\(\sqrt{3}\approx1.73\), इसलिए \(1-\sqrt{3}\approx-0.73\) है। यह (-1) और (0) के बीच है।
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यदि (A=-2.25) और (B=-0.75) हों तो संख्या रेखा पर (AB) की लंबाई कितनी है?
If (A=-2.25) and (B=-0.75), what is the length of (AB) on the number line?
#number-line
#distance
#negative-decimals
#segment
A (0.75)
B (1)
C (1.5)
D (3)
Explanation opens after your attempt
Step 1
Concept
The length is (|-0.75-(-2.25)|=1.5). Distance between negative points is also positive.
Step 2
Why this answer is correct
The correct answer is C. (1.5). The length is (|-0.75-(-2.25)|=1.5). Distance between negative points is also positive.
Step 3
Exam Tip
लंबाई (|-0.75-(-2.25)|=1.5) है। ऋणात्मक बिंदुओं के बीच भी दूरी धनात्मक होती है।
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संख्या रेखा पर \(\sqrt{32}\) किस पूर्णांक के सबसे निकट है?
On the number line, \(\sqrt{32}\) is closest to which integer?
#number-line
#estimation
#square-root
#nearest-integer
A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{32}\approx5.66\), so it is closer to (6). Compare distances for the nearest integer.
Step 2
Why this answer is correct
The correct answer is C. (6). \(\sqrt{32}\approx5.66\), so it is closer to (6). Compare distances for the nearest integer.
Step 3
Exam Tip
\(\sqrt{32}\approx5.66\) है इसलिए यह (6) के अधिक पास है। निकटतम पूर्णांक के लिए दूरी की तुलना करें।
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संख्या रेखा पर \(\sqrt{29}\) बनाने के लिए समकोण त्रिभुज की कौन सी दो लंब भुजाएं सही हो सकती हैं?
To construct \(\sqrt{29}\) on the number line, which two perpendicular sides of a right triangle can be correct?
#number-line
#construction
#pythagoras
#square-root
A (5) और (2) / (5) and (2)
B (4) और (4) / (4) and (4)
C (3) और (5) / (3) and (5)
D (6) और (1) / (6) and (1)
Explanation opens after your attempt
Correct Answer
A. (5) और (2) / (5) and (2)
Step 1
Concept
\(5^2+2^2=29\), so the hypotenuse will be \(\sqrt{29}\). Check the sum of squares of the sides.
Step 2
Why this answer is correct
The correct answer is A. (5) और (2) / (5) and (2). \(5^2+2^2=29\), so the hypotenuse will be \(\sqrt{29}\). Check the sum of squares of the sides.
Step 3
Exam Tip
\(5^2+2^2=29\), इसलिए कर्ण \(\sqrt{29}\) होगा। भुजाओं के वर्गों का योग जांचें।
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कौन सी संख्या संख्या रेखा पर \(\frac{2}{3}\) और \(\frac{3}{4}\) के बीच है?
Which number lies between \(\frac{2}{3}\) and \(\frac{3}{4}\) on the number line?
#number-line
#between
#fractions
#decimals
A (0.6)
B (0.7)
C (0.8)
D (1)
Explanation opens after your attempt
Step 1
Concept
\(\frac{2}{3}\approx0.667\) and \(\frac{3}{4}=0.75\), so (0.7) lies between them. Use decimal form for comparison.
Step 2
Why this answer is correct
The correct answer is B. (0.7). \(\frac{2}{3}\approx0.667\) and \(\frac{3}{4}=0.75\), so (0.7) lies between them. Use decimal form for comparison.
Step 3
Exam Tip
\(\frac{2}{3}\approx0.667\) और \(\frac{3}{4}=0.75\), इसलिए (0.7) बीच में है। तुलना के लिए दशमलव रूप उपयोग करें।
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संख्या रेखा पर (0.6) और (1.4) के मध्य बिंदु का मान क्या है?
What is the midpoint of (0.6) and (1.4) on the number line?
#number-line
#midpoint
#decimals
#average
A (0.8)
B (1)
C (1.2)
D (2)
Explanation opens after your attempt
Step 1
Concept
The midpoint is \(\frac{0.6+1.4}{2}=1\). The midpoint is equally distant from both ends.
Step 2
Why this answer is correct
The correct answer is B. (1). The midpoint is \(\frac{0.6+1.4}{2}=1\). The midpoint is equally distant from both ends.
Step 3
Exam Tip
मध्य बिंदु \(\frac{0.6+1.4}{2}=1\) है। मध्य बिंदु दोनों सिरों से बराबर दूरी पर होता है।
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संख्या रेखा पर (1.75) का (0) के सापेक्ष सममित बिंदु कौन सा होगा?
What will be the point symmetric to (1.75) with respect to (0) on the number line?
#number-line
#symmetry
#opposite-numbers
#decimals
A (-1.75)
B (-0.75)
C (0.75)
D (1.75)
Explanation opens after your attempt
Correct Answer
A. (-1.75)
Step 1
Concept
The symmetric point about (0) is the opposite number, so the answer is (-1.75). Opposite numbers are at equal distance.
Step 2
Why this answer is correct
The correct answer is A. (-1.75). The symmetric point about (0) is the opposite number, so the answer is (-1.75). Opposite numbers are at equal distance.
Step 3
Exam Tip
(0) के सापेक्ष सममित बिंदु विपरीत संख्या होता है इसलिए उत्तर (-1.75) है। विपरीत संख्याएं बराबर दूरी पर होती हैं।
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संख्या रेखा पर \(\sqrt{0.49}\) का सही स्थान कौन सा है?
What is the correct position of \(\sqrt{0.49}\) on the number line?
#number-line
#decimal-square-root
#perfect-square
#position
A (0.07)
B (0.7)
C (4.9)
D (7)
Explanation opens after your attempt
Step 1
Concept
Since \(0.7^2=0.49\), \(\sqrt{0.49}=0.7\). Be careful with place value in decimal squares.
Step 2
Why this answer is correct
The correct answer is B. (0.7). Since \(0.7^2=0.49\), \(\sqrt{0.49}=0.7\). Be careful with place value in decimal squares.
Step 3
Exam Tip
\(0.7^2=0.49\), इसलिए \(\sqrt{0.49}=0.7\) है। दशमलव वर्गों में स्थान मान सावधानी से देखें।
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संख्या रेखा पर \(-\sqrt{2}\), (-1.5), और (-1.3) का बढ़ता क्रम क्या है?
What is the increasing order of \(-\sqrt{2}\), (-1.5), and (-1.3) on the number line?
#number-line
#negative-numbers
#irrational-numbers
#increasing-order
A \(-1.5,-\sqrt{2},-1.3\)
B \(-\sqrt{2},-1.5,-1.3\)
C \(-1.3,-\sqrt{2},-1.5\)
D \(-1.5,-1.3,-\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(-1.5,-\sqrt{2},-1.3\)
Step 1
Concept
\(\sqrt{2}\approx1.41\), so \(-1.5<-\sqrt{2}<-1.3\). For negative numbers, the farther left number is smaller.
Step 2
Why this answer is correct
The correct answer is A. \(-1.5,-\sqrt{2},-1.3\). \(\sqrt{2}\approx1.41\), so \(-1.5<-\sqrt{2}<-1.3\). For negative numbers, the farther left number is smaller.
Step 3
Exam Tip
\(\sqrt{2}\approx1.41\), इसलिए \(-1.5<-\sqrt{2}<-1.3\) है। ऋणात्मक संख्याओं में अधिक बाईं संख्या छोटी होती है।
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संख्या रेखा पर \(-\frac{7}{3}\) की (0) से दूरी कितनी है?
What is the distance of \(-\frac{7}{3}\) from (0) on the number line?
#number-line
#distance
#absolute-value
#negative-fraction
A \(-\frac{7}{3}\)
B \(\frac{7}{3}\)
C \(\frac{3}{7}\)
D \(\frac{10}{3}\)
Explanation opens after your attempt
Correct Answer
B. \(\frac{7}{3}\)
Step 1
Concept
Distance from (0) is magnitude, so \(\left|-\frac{7}{3}\right|=\frac{7}{3}\). Distance is never negative.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{7}{3}\). Distance from (0) is magnitude, so \(\left|-\frac{7}{3}\right|=\frac{7}{3}\). Distance is never negative.
Step 3
Exam Tip
(0) से दूरी परिमाण होती है इसलिए \(\left|-\frac{7}{3}\right|=\frac{7}{3}\) है। दूरी ऋणात्मक नहीं होती।
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संख्या रेखा पर (0.125) किस भिन्न के समान बिंदु है?
On the number line, (0.125) is the same point as which fraction?
#number-line
#decimals
#fractions
#equivalent
A \(\frac{1}{4}\)
B \(\frac{1}{8}\)
C \(\frac{1}{10}\)
D \(\frac{1}{12}\)
Explanation opens after your attempt
Correct Answer
B. \(\frac{1}{8}\)
Step 1
Concept
\(0.125=\frac{125}{1000}=\frac{1}{8}\). Start with denominator (10), (100), or (1000), then simplify.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{1}{8}\). \(0.125=\frac{125}{1000}=\frac{1}{8}\). Start with denominator (10), (100), or (1000), then simplify.
Step 3
Exam Tip
\(0.125=\frac{125}{1000}=\frac{1}{8}\) है। दशमलव को हर (10), (100), या (1000) से शुरू करके सरल करें।
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संख्या रेखा पर \(-\sqrt{11}\) किस दो पूर्णांकों के बीच होगा?
Between which two integers will \(-\sqrt{11}\) lie on the number line?
#number-line
#negative-root
#irrational-numbers
#interval
A (-2) और (-1) / (-2) and (-1)
B (-3) और (-2) / (-3) and (-2)
C (-4) और (-3) / (-4) and (-3)
D (3) और (4) / (3) and (4)
Explanation opens after your attempt
Correct Answer
C. (-4) और (-3) / (-4) and (-3)
Step 1
Concept
\(\sqrt{11}\) lies between (3) and (4), so \(-\sqrt{11}\) lies between (-4) and (-3). The negative sign changes the side.
Step 2
Why this answer is correct
The correct answer is C. (-4) और (-3) / (-4) and (-3). \(\sqrt{11}\) lies between (3) and (4), so \(-\sqrt{11}\) lies between (-4) and (-3). The negative sign changes the side.
Step 3
Exam Tip
\(\sqrt{11}\) (3) और (4) के बीच है इसलिए \(-\sqrt{11}\) (-4) और (-3) के बीच होगा। ऋणात्मक चिन्ह दिशा बदल देता है।
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